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Sacred Mathematics:
Japanese Temple Geometry
Fukagawa Hidetoshi & Tony Rothman
With a foreword by Freeman Dyson

Winner of the 2008 PROSE Award in Mathematics, Association of American Publishers

Hardcover | 2008 | $62.50 | £52.95 | ISBN: 9780691127453
392 pp. | 8 x 10 | 16 color illus. 150 line illus.
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Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree. During that time, a unique brand of homegrown mathematics flourished, one that was completely uninfluenced by developments in Western mathematics. People from all walks of life--samurai, farmers, and merchants--inscribed a wide variety of geometry problems on wooden tablets called sangaku and hung them in Buddhist temples and Shinto shrines throughout Japan. Sacred Mathematics is the first book published in the West to fully examine this tantalizing--and incredibly beautiful--mathematical tradition.

Fukagawa Hidetoshi and Tony Rothman present for the first time in English excerpts from the travel diary of a nineteenth-century Japanese mathematician, Yamaguchi Kanzan, who journeyed on foot throughout Japan to collect temple geometry problems. The authors set this fascinating travel narrative--and almost everything else that is known about temple geometry--within the broader cultural and historical context of the period. They explain the sacred and devotional aspects of sangaku, and reveal how Japanese folk mathematicians discovered many well-known theorems independently of mathematicians in the West--and in some cases much earlier. The book is generously illustrated with photographs of the tablets and stunning artwork of the period. Then there are the geometry problems themselves, nearly two hundred of them, fully illustrated and ranging from the utterly simple to the virtually impossible. Solutions for most are provided.

A unique book in every respect, Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries.


"Now Fukagawa Hidetoshi, a mathematics teacher, and writer Tony Rothman present a collection of Sangaku problems in their book, Sacred Mathematics. The puzzles range from simple algebra within the grasp of any intermediate-school student, to challenging problems that require graduate-school mathematics to solve. Copious illustrations and many detailed solutions show the scope, complexity, and beauty of what was tackled in Japan during the Tokugawa shogunate."--Peter J. Lu, Nature

"Fascinating and beautiful book."--Physics World

"This book is the most thorough (and beautiful) account of Japanese temple geometry (sangaku) available."--Paul J. Campbell, Mathematics Magazine

"The difficult problems with complete solutions and rich commentary that comprise the heart of this book will interest every mathematics student."--Choice

"This is a marvelous book. Good books are not just written or compiled, they are crafted. Sacred Mathematics is a well crafted work that combines mathematics, history and cultural considerations into an intriguing narrative. . . . The writing style is appealing and the organization of material excellent. Princeton University Press must be congratulated on producing this quality publication and offering it at an agreeable price. This book is highly recommended for personal reading and library acquisition. It should be especially appealing to problem solvers."--Frank J. Swetz, Convergence

"A unique book in every respect. Sacred Mathematics demonstrates how mathematical thinking can vary by culture yet transcend cultural and geographic boundaries."--International Institute for Asian Studies Newsletter

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Table of Contents:

Foreword by Freeman Dyson ix
Preface by Fukagawa Hidetoshi xiii
Preface by Tony Rothman xv
Acknowledg ments xix
What Do I Need to Know to Read This Book? xxi
Notation xxv
Chapter 1: Japan and Temple Geometry 1
Chapter 2: The Chinese Foundation of Japanese Mathematics 27
Chapter 3: Japa nese Mathematics and Mathematicians
of the Edo Period 59
Chapter 4: Easier Temple Geometry Problems 89
Chapter 5: Harder Temple Geometry Problems 145
Chapter 6: Still Harder Temple Geometry Problems 191
Chapter 7: The Travel Diary of Mathematician Yamaguchi Kanzan 243
Chapter 8: East and West 283
Chapter 9: The Mysterious Enri 301
Chapter 10: Introduction to Inversion 313
For Further Reading 337
Index 341

This book has been translated into:

  • Japanese

Other Princeton books authored or coauthored by Tony Rothman:


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File created: 8/1/2017

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